CN117590360A - Color ratio calibration method for multi-wavelength laser radar - Google Patents

Color ratio calibration method for multi-wavelength laser radar Download PDF

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CN117590360A
CN117590360A CN202410053384.7A CN202410053384A CN117590360A CN 117590360 A CN117590360 A CN 117590360A CN 202410053384 A CN202410053384 A CN 202410053384A CN 117590360 A CN117590360 A CN 117590360A
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wavelength
height
wavelengths
laser radar
calculating
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CN117590360B (en
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陶玥
赵志强
徐艳丽
况志强
唐雅慧
赵舒文
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Weather Modification Center Of China Meteorological Administration
Hefei Zhongke Guangbo Quantum Technology Co ltd
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Weather Modification Center Of China Meteorological Administration
Hefei Zhongke Guangbo Quantum Technology Co ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/497Means for monitoring or calibrating
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/4802Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02ATECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention relates to laser radar calibration, in particular to a multi-wavelength laser radar color ratio calibration method, which is used for determining a calibration constant to be calibrated; acquiring target echo signals of two wavelengths in a wavelength pair participating in laser radar color ratio calculation after background subtraction; respectively calculating the signal-to-noise ratio of echo signals of two wavelengths from the effective initial height of the wavelength pair, and judging the effective detection distance of the color ratio of the laser radar; calculating the slope of the distance square correction signal of the clean atmosphere altitude interval after logarithm is taken, and obtaining slope sequences corresponding to two wavelengths; determining a calibration signal containing a clean atmosphere altitude interval based on slope sequences corresponding to the two wavelengths; calculating radar constants of two wavelengths based on the calibration signals, and calculating to obtain the calibration constants; the technical scheme provided by the invention can effectively overcome the defect that the inversion result is error due to the fact that the color ratio of the multi-wavelength laser radar cannot be accurately calibrated in the prior art.

Description

Color ratio calibration method for multi-wavelength laser radar
Technical Field
The invention relates to laser radar calibration, in particular to a multi-wavelength laser radar color ratio calibration method.
Background
The multi-wavelength laser radar uses radiation signals of interaction of laser and atmosphere to remotely sense atmosphere, is one of important means of cloud and aerosol detection, generally has a plurality of emission wavelengths of 355nm, 532nm, 1064nm and the like, and can detect echo signals of a plurality of meter scattering channels and Raman scattering channels. The physical characteristics of aerosol in the atmosphere are detected and identified by utilizing multi-wavelength meter scattering, polarization, nitrogen molecular back scattering and the like of laser, and the method is used for inverting the vertical profile, cloud base and the like of the aerosol and cloud drop spectrum, and specifically comprises the following steps: aerosol and cloud extinction coefficient profiles, aerosol and cloud backscatter coefficient profiles, aerosol and cloud extinction/cloud backscattering ratio profiles, aerosol and cloud particle profile, aerosol and cloud backscattering signal depolarization ratio profiles, aerosol and cloud backscattering signal color ratio profiles, and the like. The aerosol and cloud back scattering signal color ratio profile (attenuated color ratio, ACR) can represent the relative size of aerosol particles, and the types of the aerosol and cloud particles can be effectively identified based on multiple parameters such as depolarization ratio, color ratio and the like.
The color ratio of the laser radar is a dimensionless parameter and can be calculated from echo signals of any two different emission wavelengths, such as 355nm and 1064nm wavelength pairs, 355nm and 532nm wavelength pairs, 532nm and 1064nm wavelength pairs, and the like.
Due to the lack of a calibration method, radar system parameters are used for calculating the color ratio of the laser radarUsually isThe method is set at will, and therefore, under the condition that the same airspace is detected at the same moment, larger absolute value differences exist in the observation results of different factories and even different batches of laser radars of the same manufacturer. Furthermore, the radar system parameters->The absolute value of the color ratio for targets of the same nature (e.g., clouds, dust, etc.) may also change, such as increased window contamination, changes in transmittance at different wavelengths, etc. The color ratio of the multi-wavelength laser radar is calibrated, the influence of a specific wavelength radar constant is eliminated, and the method has important significance for analyzing the relative size of aerosol particles by utilizing the color ratio of the laser radar.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides a multi-wavelength laser radar color ratio calibration method, which can effectively overcome the defect that the inversion result is error due to the fact that the multi-wavelength laser radar color ratio cannot be accurately calibrated in the prior art.
In order to achieve the above purpose, the invention is realized by the following technical scheme:
a color ratio calibration method of a multi-wavelength laser radar comprises the following steps:
s1, determining a calibration constant to be calibrated;
s2, acquiring target echo signals of two wavelengths in a wavelength pair participating in laser radar color ratio calculation after background subtraction;
s3, respectively calculating signal-to-noise ratios of echo signals of two wavelengths from the effective initial height of the wavelength pair, and judging the effective detection distance of the laser radar color ratio;
s4, calculating the slope of the distance square correction signal of the clean atmosphere height interval after logarithm is taken, and obtaining slope sequences corresponding to two wavelengths;
s5, determining a calibration signal containing a clean atmosphere height interval based on slope sequences corresponding to the two wavelengths;
s6, calculating radar constants of two wavelengths based on the calibration signals, and calculating to obtain the calibration constants.
Preferably, determining the calibration constant to be calibrated in S1 includes:
for any two wavelengths, the laser radar color ratio at height zThe following formula was used for calculation:
wherein,is the wavelength at the height z->Distance square correction signal, < >>Is the wavelength at the height z->Distance square correction signal, < >>The radar system parameters are the calibration constants required to be calibrated.
Preferably, the step S2 of obtaining the target echo signal after subtracting the background from the echo signals of two wavelengths in the wavelength pair involved in the calculation of the color ratio of the lidar includes:
taking the average value of the echo signals of 20 km-30 km of each channel as a background value, and subtracting the background value of each channel from the echo signals of 0-30 km of the corresponding channel in sequence to obtain target echo signals of the two wavelengths at the height z after subtracting the background、/>
Preferably, in S3, the signal-to-noise ratio of the echo signals of the two wavelengths is calculated from the wavelength pair effective initial height, including:
calculating the wavelength at height z usingIs>
Wherein,is the wavelength at the height z->Target echo signal,/,>for wavelength->Is calculated by the following formula:
in the above-mentioned method, the step of,for wavelength->The ith data in the echo signal sequence of (a), m is the starting point of the data sequence for calculating the signal noise floor, n is the number of data for calculating the signal noise floor, < ->When m-m+n is taken as i +.>Is a mathematical average of (a).
Preferably, determining the effective detection distance of the color ratio of the lidar in S3 includes:
if the signal-to-noise ratio of the echo signal of any one wavelength at the height z is smaller than 3, judging that the height z at the moment is the effective detection distance of the laser radar color ratio;
at the height ofIf yes, S4 is entered; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
Preferably, in S4, calculating the slope of the log of the distance square correction signal in the clean air altitude interval to obtain a slope sequence corresponding to two wavelengths, including:
s41, the following laser radar equation is provided:
wherein,for wavelength->Radar constant of (c) in clean atmosphere altitude interval, aerosol backscattering coefficientAerosol extinction coefficient->,/>Any one of the heights within the range of 0~z;
s42, evolution of a laser radar equation is as follows:
(1),
wherein,is the wavelength at the height z->Is calculated using the following equation:
is the wavelength at the height z->The corresponding molecular backscatter coefficients are calculated using the following formula:
is the wavelength at the height z->The corresponding molecular extinction coefficient is calculated by the following formula:
s43, taking the logarithm of the left and right of the (1):
(2),
s44, deriving the height z from the left and right of the step (2):
s45, based on radar distance resolutionCalculating the +.about.two wavelengths within the range of 5 km-8 km>Obtaining the actually measured slope sequence corresponding to the two wavelengths>、/>Then calculate +.>Obtaining a theoretical slope sequence corresponding to two wavelengths +.>、/>Actually measured slope sequence corresponding to two wavelengths +.>、/>And the theoretical slope sequence>、/>The number of data of (a) is->
Preferably, determining the calibration signal including the clean atmosphere altitude interval based on the slope sequences corresponding to the two wavelengths in S5 includes:
s51, calculating wavelength by adopting the following methodIs>And theoretical slope sequence->Error between corresponding slope values:
(3),
wherein,for wavelength->Is>And theoretical slope sequence->Error between the b-th slope values, in->For the actual measurement of the slope sequence->B slope value of (b), d>For a theoretical slope sequenceA b-th slope value of (b);
s52, when all errors between the corresponding slope values in the actual measurement slope sequence and the theoretical slope sequence of the two wavelengths are calculated based on the formula (3)、/>When the air is less than 10%, the air is judged to be a clean air height interval within the range of 5km to 8km,and determines the corresponding +.>、/>A calibration signal including a clean atmosphere altitude interval; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
Preferably, the step S6 of calculating radar constants of two wavelengths based on the calibration signal and calculating the calibration constant includes:
s61, calculating the wavelength at the height h by combining (1) based on a calibration signal containing the clean atmosphere height intervalRadar constant of->
(4),
Wherein the range of the height h is a clean atmosphere height interval, namely 5km to 8km,any height in the range of 5 km-h;
s62, calculating to obtain wavelength at height h based on (4)Radar constant of->And wavelength at height hRadar constant of->
S63, respectively taking in the clean atmosphere height interval、/>To obtain the radar constant of the corresponding two wavelengths +.>、/>
S64, calculating a calibration constant by adopting the following method
Compared with the prior art, the color ratio calibration method of the multi-wavelength laser radar has the following beneficial effects:
1) The method fills the blank of a multi-wavelength laser radar color ratio calibration method, unifies the standard, and can further unify the color ratio size threshold intervals of aerosol particles with different particle diameters on the basis;
2) The method can be used for calibrating in offline analysis, and can be used for calibrating periodically in the continuous operation process of the laser radar, so that the parameters of a radar system are eliminatedThe influence on the inversion of the color ratio of the laser radar caused by the change of the laser radar (such as the factors of energy reduction difference of lasers with different wavelengths, window pollution aggravation, transmittance change of different wavelengths and the like);
3) The method can greatly improve the uniformity and stability of the color ratio inversion result of the laser radar, obtain more reliable atmospheric observation data with high space-time resolution, and provide important observation data for scientific research services such as weather forecast, weather artificially influenced and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It is evident that the drawings in the following description are only some embodiments of the present invention and that other drawings may be obtained from these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in FIG. 1, the method for calibrating the color ratio of the multi-wavelength laser radar comprises the following steps of S1, determining a calibration constant to be calibrated:
for any two wavelengths, the laser radar color ratio at height zThe following formula was used for calculation:
wherein,is the wavelength at the height z->Distance square correction signal, < >>Is the wavelength at the height z->Distance square correction signal, < >>The radar system parameters (influenced by factors such as energy reduction difference of lasers with different wavelengths, window pollution aggravation, transmittance change of different wavelengths and the like) are calibrated constants which need to be calibrated.
S2, acquiring target echo signals of two wavelengths in a wavelength pair participating in laser radar color ratio calculation after background subtraction, wherein the method specifically comprises the following steps:
taking the average value of the echo signals of 20 km-30 km of each channel as a background value, and subtracting the background value of each channel from the echo signals of 0-30 km of the corresponding channel in sequence to obtain target echo signals of the two wavelengths at the height z after subtracting the background、/>
S3, respectively calculating the signal-to-noise ratio of echo signals of the two wavelengths from the effective initial height of the wavelength pair, and judging the effective detection distance of the laser radar color ratio.
1) Calculating echo signal to noise ratios of two wavelengths, respectively, from the wavelength pair effective initial height, comprising:
calculating the wavelength at height z usingIs>
Wherein,is the wavelength at the height z->Target echo signal,/,>for wavelength->Is calculated by the following formula:
in the above-mentioned method, the step of,for wavelength->The ith data in the echo signal sequence of (a), m is the starting point of the data sequence for calculating the signal noise floor, n is the number of data for calculating the signal noise floor, < ->When m-m+n is taken as i +.>Is a mathematical average of (a).
2) Determining an effective detection distance of a laser radar color ratio, comprising:
if the signal-to-noise ratio of the echo signal of any one wavelength at the height z is smaller than 3, judging that the height z at the moment is the effective detection distance of the laser radar color ratio;
at the height ofIf yes, S4 is entered; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
S4, calculating the slope of the distance square correction signal in the clean atmosphere height interval after taking the logarithm to obtain a slope sequence corresponding to two wavelengths, wherein the slope sequence specifically comprises the following steps:
s41, the following laser radar equation is provided:
wherein,for wavelength->Radar constant of (c) in clean atmosphere altitude interval, aerosol backscattering coefficientAerosol extinction coefficient->,/>Any one of the heights within the range of 0~z;
s42, evolution of a laser radar equation is as follows:
(1),
wherein,is the wavelength at the height z->Is calculated using the following equation:
is the wavelength at the height z->The corresponding molecular backscatter coefficients are calculated using the following formula:
is the wavelength at the height z->The corresponding molecular extinction coefficient is calculated by the following formula:
s43, taking the logarithm of the left and right of the (1):
(2)
s44, deriving the height z from the left and right of the step (2):
s45, based on radar distance resolutionCalculating the +.about.two wavelengths within the range of 5 km-8 km>Obtaining the actually measured slope sequence corresponding to the two wavelengths>、/>Then calculate +.>Obtaining a theoretical slope sequence corresponding to two wavelengths +.>、/>Actually measured slope sequence corresponding to two wavelengths +.>、/>And the theoretical slope sequence>、/>The number of data of (a) is->
S5, determining a calibration signal containing a clean atmosphere height interval based on slope sequences corresponding to two wavelengths, wherein the calibration signal comprises the following specific steps:
s51, calculating wavelength by adopting the following methodIs>And theoretical slope sequence->Error between corresponding slope values:
(3),
wherein,for wavelength->Is>And theoretical slope sequence->Error between the b-th slope values, in->For the actual measurement of the slope sequence->B slope value of (b), d>For a theoretical slope sequenceA b-th slope value of (b);
s52, when all errors between the corresponding slope values in the actual measurement slope sequence and the theoretical slope sequence of the two wavelengths are calculated based on the formula (3)、/>When the air is less than 10%, judging that the air is in a clean air height interval within a range of 5 km-8 km, and determining corresponding +.>、/>A calibration signal including a clean atmosphere altitude interval; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
S6, calculating radar constants of two wavelengths based on the calibration signals, and calculating to obtain the calibration constants, wherein the method specifically comprises the following steps:
s61, marking based on altitude interval including clean atmosphereFixed signal and combined (1) to calculate wavelength at height hRadar constant of->
(4),
Wherein the range of the height h is a clean atmosphere height interval, namely 5km to 8km,any height in the range of 5 km-h;
s62, calculating to obtain wavelength at height h based on (4)Radar constant of->And wavelength at height hRadar constant of->
S63, respectively taking in the clean atmosphere height interval、/>To obtain the radar constant of the corresponding two wavelengths +.>、/>
S64, calculating a calibration constant by adopting the following method
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. A color ratio calibration method of a multi-wavelength laser radar is characterized in that: the method comprises the following steps:
s1, determining a calibration constant to be calibrated;
s2, acquiring target echo signals of two wavelengths in a wavelength pair participating in laser radar color ratio calculation after background subtraction;
s3, respectively calculating signal-to-noise ratios of echo signals of two wavelengths from the effective initial height of the wavelength pair, and judging the effective detection distance of the laser radar color ratio;
s4, calculating the slope of the distance square correction signal of the clean atmosphere height interval after logarithm is taken, and obtaining slope sequences corresponding to two wavelengths;
s5, determining a calibration signal containing a clean atmosphere height interval based on slope sequences corresponding to the two wavelengths;
s6, calculating radar constants of two wavelengths based on the calibration signals, and calculating to obtain the calibration constants.
2. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 1, wherein the method comprises the following steps: s1, determining a calibration constant to be calibrated, wherein the calibration constant comprises the following steps:
for the followingLaser radar color ratio at any two wavelengths and height zThe following formula was used for calculation:
wherein,is the wavelength at the height z->Distance square correction signal, < >>Is the wavelength at the height z->Distance square correction signal, < >>The radar system parameters are the calibration constants required to be calibrated.
3. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 2, wherein the method comprises the following steps: s2, acquiring target echo signals of two wavelengths in a wavelength pair participating in laser radar color ratio calculation after background subtraction, wherein the target echo signals comprise:
taking the average value of the echo signals of 20 km-30 km of each channel as a background value, and subtracting the background value of each channel from the echo signals of 0-30 km of the corresponding channel in sequence to obtain target echo signals of the two wavelengths at the height z after subtracting the background、/>
4. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 3, wherein the method comprises the following steps: in S3, respectively calculating signal-to-noise ratios of echo signals of two wavelengths from the effective initial height of the wavelength pair, including:
calculating the wavelength at height z usingIs>
Wherein,is the wavelength at the height z->Target echo signal,/,>for wavelength->Is calculated by the following formula:
in the above-mentioned method, the step of,for wavelength->Is set in the form of an echo signal of (a)The ith data in the sequence, m is the starting point of the data sequence for calculating the signal noise floor, n is the number of data for calculating the signal noise floor,/day>When m-m+n is taken as i +.>Is a mathematical average of (a).
5. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 4, wherein the method comprises the following steps: s3, judging the effective detection distance of the laser radar color ratio, which comprises the following steps:
if the signal-to-noise ratio of the echo signal of any one wavelength at the height z is smaller than 3, judging that the height z at the moment is the effective detection distance of the laser radar color ratio;
at the height ofIf yes, S4 is entered; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
6. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 5, wherein the method comprises the following steps: s4, calculating the slope of the distance square correction signal of the clean atmosphere height interval after logarithm is taken, and obtaining a slope sequence corresponding to two wavelengths, wherein the slope sequence comprises the following steps:
s41, the following laser radar equation is provided:
wherein,for wavelength->Radar constant of (C) in clean atmosphereDegree interval, aerosol backscattering coefficientAerosol extinction coefficient->,/>Any one of the heights within the range of 0~z;
s42, evolution of a laser radar equation is as follows:
(1),
wherein,is the wavelength at the height z->Is calculated using the following equation:
is the wavelength at the height z->The corresponding molecular backscatter coefficients are calculated using the following formula:
is the wavelength at the height z->The corresponding molecular extinction coefficient is calculated by the following formula:
s43, taking the logarithm of the left and right of the (1):
(2),
s44, deriving the height z from the left and right of the step (2):
s45, based on radar distance resolutionCalculating the +.about.two wavelengths within the range of 5 km-8 km>Obtaining the actually measured slope sequence corresponding to the two wavelengths>、/>Then calculate +.>Obtaining a theoretical slope sequence corresponding to two wavelengths +.>、/>Actually measured slope sequence corresponding to two wavelengths +.>、/>And the theoretical slope sequence>、/>The number of data of (a) is->
7. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 6, wherein the method comprises the following steps: s5, determining a calibration signal containing a clean atmosphere altitude interval based on slope sequences corresponding to two wavelengths, wherein the calibration signal comprises the following components:
s51, calculating wavelength by adopting the following methodIs>And theoretical slope sequence->Error between corresponding slope values:
(3),
wherein,for wavelength->Is>And theoretical slope sequence->Error between the b-th slope values, in->For the actual measurement of the slope sequence->B slope value of (b), d>For the theoretical slope sequence>A b-th slope value of (b);
s52, when all errors between the corresponding slope values in the actual measurement slope sequence and the theoretical slope sequence of the two wavelengths are calculated based on the formula (3)、/>When the air is less than 10%, judging that the air is in a clean air height interval within a range of 5 km-8 km, and determining corresponding +.>、/>A calibration signal including a clean atmosphere altitude interval; otherwise, the wavelength pairs participating in the calculation of the color ratio of the laser radar are reselected, and S2 is returned.
8. The method for calibrating the color ratio of the multi-wavelength laser radar according to claim 7, wherein the method comprises the following steps: s6, calculating radar constants of two wavelengths based on the calibration signals, and calculating to obtain the calibration constants, wherein the method comprises the following steps:
s61, calculating the wavelength at the height h by combining (1) based on a calibration signal containing the clean atmosphere height intervalRadar constant of->
(4),
Wherein the range of the height h is a clean atmosphere height interval, namely 5km to 8km,any height in the range of 5 km-h;
s62, calculating to obtain wavelength at height h based on (4)Radar constant of->And wavelength at height h +.>Radar constant of->
S63, respectively taking in the clean atmosphere height interval、/>To obtain the radar constant of the corresponding two wavelengths +.>、/>
S64, calculating a calibration constant by adopting the following method
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